Second‐order, loosely coupled methods for fluid‐poroelastic material interaction
Second‐order, loosely coupled methods for fluid‐poroelastic material interaction
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DOI：
10.1002/num.22452
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发表时间：
2019-12
影响因子：
3.9
通讯作者：
Oyekola Oyekole;M. Bukač
中科院分区：
文献类型：
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作者：
Oyekola Oyekole;M. Bukač
这项工作的重点是模拟不可压缩的粘性流体和孔粘弹性材料之间的相互作用。流体流动用时间相关的Stokes方程来描述，孔隙弹性材料用Biot模型来描述。用线性Kelvin-Voigt模型将粘弹性纳入方程。我们为耦合问题引入了两种新颖的、非迭代的、分区的数值格式。第一种方法使用二阶后向微分公式（BDF2）进行隐式积分，同时使用二阶外推公式显式地处理界面项。第二种方法是Crank-Nicolson和Leap‐Frog （CNLF）方法，其中Crank-Nicolson方法用于隐式地在时间上推进解，而耦合项则由Leap‐Frog积分显式地逼近。证明了BDF2方法在时间上是无条件稳定和一致稳定的，而CNLF方法在CFL条件下是稳定的。通过数值模拟对两种方案进行了验证。两种方法在时间上都具有二阶收敛性。较长时间的模拟表明，该解决方案中的误差仍然是有限的。数值算例中包括了孔粘弹性和孔弹性结构的情况。
This work focuses on modeling the interaction between an incompressible, viscous fluid and a poroviscoelastic material. The fluid flow is described using the time‐dependent Stokes equations, and the poroelastic material using the Biot model. The viscoelasticity is incorporated in the equations using a linear Kelvin–Voigt model. We introduce two novel, noniterative, partitioned numerical schemes for the coupled problem. The first method uses the second‐order backward differentiation formula (BDF2) for implicit integration, while treating the interface terms explicitly using a second‐order extrapolation formula. The second method is the Crank–Nicolson and Leap‐Frog (CNLF) method, where the Crank–Nicolson method is used to implicitly advance the solution in time, while the coupling terms are explicitly approximated by the Leap‐Frog integration. We show that the BDF2 method is unconditionally stable and uniformly stable in time, while the CNLF method is stable under a CFL condition. Both schemes are validated using numerical simulations. Second‐order convergence in time is observed for both methods. Simulations over a longer period of time show that the errors in the solution remain bounded. Cases when the structure is poroviscoelastic and poroelastic are included in numerical examples.